Low complexity method and apparatus to append a cyclic extension to a continuous phase modulation (cpm) signal

ABSTRACT

The present invention provides a new and unique method and apparatus for cyclically extending a continuous phase modulation (CPM) block, which features transmitting each information symbol and its antipodal counterpart in any order within a data portion of the continuous phase modulation block. The continuous phase modulation block includes a sequence of N/2 M-ary information symbols that are spread over N symbol intervals, and the cyclic extension includes the first G M-ary symbols sent in the data portion of the block being appended to the continuous phase modulation block.

BACKGROUND OF THE INVENTION

1. Field of Invention

The present invention is related to a method and apparatus forcyclically extending a Continuous Phase Modulation (CPM) signal; andmore particularly, is related to a method and apparatus for cyclicallyextending a CPM signal in a high speed wireless packet network such asthat set forth in the IEEE 802.16e Standard for wireless MetropolitanArea Network (MAN) technology.

2. Description of Related Art

Orthogonal Frequency Division Multiplexing (OFDM) transmission schemesare a well known in the art for transmitting data in broadbandmulti-user communications systems and network, as well as other knownsystems and networks, and was first introduced as a means ofcounteracting channel-induced linear distortions encountered whentransmitting over a dispersive radio channel. See L. Hanzo, et al.,“OFDM and MC-CDMA for Broadband Multi-User Communications, WLANs andBroadcasting,” J. Wiley & Sons, Ltd., 2004; as well as A. Bahai et al.,“Multi-Carrier Digital Communications Theory and Applications of OFDM”,2nd Ed., Springer Science and Business, Inc. 2004.

For such OFDM transmission schemes, inter-symbol interference (ISI) andinter-carrier interference (ICI) can be removed at the receiver byadding a cyclic guard interval and a cyclic prefix to the time-domaintransmitted signal. This is accomplished by pre-pending a certain numberof the ending data vector to the beginning of the OFDM symbol (or,equivalently, by appending a certain number of the beginning data vectorto the end of the OFDM symbol). If the guard interval is longer induration than the channel's impulse response, then each sub-carrier willappear to have passed through a flat fading channel. Consequently, thereceiver can exploit the cyclic shift properties of the Discrete FourierTransform (DFT) to significantly reduce the complexity of frequencydomain equalization (FDE) techniques.

For example, FIG. 1 shows blocks of data 6, 8 having cyclic extensions10, 12 postfixed thereon in relation to corresponding blocks of data 13,15 having cyclic extensions 14, 16 prefixed thereon. When transmitted,each block of data is linearly convolved with the channel. By adding thecyclic extension (prefix or postfix) to each block, one can make thelinear convolution between the block and the channel appear to be acircular convolution if the length of the guard interval exceeds theimpulse response length of the channel. In the frequency domain, one canimplement a single-tap channel equalizer at each frequency. Thistechnique is well known for OFDM-based communications networks andsystems and, more recently, for single-carrier systems. It has onlyrecently been considered for CPM-based applications. In FIG. 1, there isa window (L . . . G) over which the FFT window may start. As long anNk-point FFT is taken (N data symbols/block and k samples/symbol), onecan obtain an identical receiver output.

Moreover, DFT-based SC-FDE (Single-Carrier FDE) techniques have onlyrecently been applied to Continuous Phase Modulation (CPM) systems. Forthe purpose of understanding the invention that is discussed herein, CPMis summarized and characterized as follows: Over the nth symbolinterval, a binary single-h CPM waveform can be expressed as

$\begin{matrix}{{{s\left( {t,a,h} \right)} = {\exp \left\{ {j\; 2\pi \; h{\sum\limits_{i = {- \infty}}^{n}{I_{i}{q\left( {t - {iT}} \right)}}}} \right\}}},{{nT} \leq t < {\left( {n + 1} \right)T}},} & (1)\end{matrix}$

where T denotes the symbol duration, I_(i)∈ {±1} are the binary databits and h is the modulation index. The phase function, q(t), is theintegral of the frequency function, f(t), which is zero outside of thetime interval (0,LT) and which is scaled such that

$\begin{matrix}{{\int_{0}^{LT}{{f(\tau)}{\tau}}} = {{q({LT})} = {\frac{1}{2}.}}} & (2)\end{matrix}$

An M-ary single-h CPM waveform is the logical extension of the binarysingle-h case in which the information symbols are now multi-level:i.e., I_(i)∈ {±1, ±3, . . . , ±(M−1)}. Usually, M is selected to be aneven number. However, it is noted that other alphabets are possible (andcan also be used with this invention). For example, M can be odd or thealphabet can include zero—i.e. I_(i)∈ {0, ±1, ±3, . . . , ±(M−1)}. Theonly restriction is that the alphabet contains an element and itsantipodal counterpart. Finally, an M-ary multi-h CPM waveform can bewritten as

$\begin{matrix}{{{s\left( {t,I,h} \right)} = {\exp \left\{ {{j2\pi}{\sum\limits_{i = {- \infty}}^{n}\; {I_{i}h_{{(i)}_{J}}{q\left( {t - {iT}} \right)}}}} \right\}}},{{nT} \leq t < {\left( {n + 1} \right){T.}}}} & (3)\end{matrix}$

Typically, I_(i)∈ {±1, ±3, . . . , ±(M−1)} (M even). However, there isno restriction to this particular alphabet and M can even be odd, asmentioned earlier. Typically, the modulation index cycles through a setof J values: h∈ {h₀ . . . h_(J−1)} and so (i)_(J) denotes “i mod J”. Theexpression in (3) may also be written as:

$\begin{matrix}{{s\left( {t,a,h} \right)} = {\exp \left\{ {j\left( {\theta_{n - L} + {2\pi {\sum\limits_{i = 0}^{L - 1}\; {I_{n - i}h_{{({n - i})}_{J}}{q\left( {t - {\left( {n - i} \right)T}} \right)}}}}} \right\}} \right.}} & (4)\end{matrix}$

The phase state,

$\theta_{n - L} = {\pi {\sum\limits_{i = {- \infty}}^{n - L}{I_{i}h_{{(i)}_{J}}{mod}\; 2\pi}}}$

determines the contribution of the symbols for which the phase functionhas reached its final constant value of one half.

However, when applying such DFT-based SC-FDE techniques to CPM systems,some issues have developed. Since the CPM waveform signal is supposed tohave a continuous phase, one cannot simply append a cyclic extension atthe end or beginning of a data block. FIG. 2 shows an example of a blindintroduction of a cyclic extension, which can destroy the continuousphase property of the CPM waveform signal. If the wrong cyclic postfixis appended to a CPM waveform, the phase would become discontinuous,which results in expansion of the signal bandwidth and a reduction inspectral efficiency. In effect, when pre-pending or appending the cyclicextension to the CPM waveform, care must be taken in order to maintainphase continuity.

One approach for appending a cyclic extension to CPM block transmissionsis to insert special data-dependent symbols (“channel” or “tail”symbols) into the data portion of the CPM transmission block. Theinclusion of these special symbols allows the transmitter to repeat thedata in a cyclic extension without destroying the continuous phaseproperty of the signal. However, these “channel” symbols, which arecalculated based on past observations, must either be computed on ablock-by-block basis or determined by using a table-lookup in order tomap a particular sequence of observed symbols to the required “channel”symbol sequence. In addition, since they are data-dependent, the actualnumber of “channel” bits that are needed may vary from block to block.Simple approaches exist for constructing the “tail” bits for binarysingle-h CPM systems, but no one has provided a general, low complexitysolution for M-ary multi-h CPM.

Detailed Discussion of Known Techniques for Solving the CPM PhaseContinuity Problem

The following is a detailed discussion of known techniques for solvingthe phase continuity problem:

The first technique is set forth in Jun Tan and Gordon L. Stüber,“Frequency Domain Equalization for Continuous Phase Modulation”,accepted for publication in the IEEE Transactions in WirelessCommunications, where Tan and Stüber investigate various approaches forapplying SC-FDE to binary single-h CPM block transmissions that havecyclic extensions. In their approach, the transmitter prepends alength-G cyclic prefix to the data block, where G equals or exceeds themaximum expected channel length. The total block length, including thedata and the cyclic prefix, is N+G, where N denotes the size of the dataportion of the block (including “tail” bits), as shown in FIG. 3.

In order to facilitate their analysis, they use Rimoldi's “tilted-phase”representation for CPM, as set forth in Bixio Rimoldi, “A DecompositionApproach to CPM”, IEEE Transactions on Information Theory, Vol. 34, No.2, March 1988, which models CPM as a Continuous Phase Encoder (whichresembles a convolutional encoder) followed by a memory-less modulator.

In order to ensure phase continuity when the cyclic prefix is used, theyforce the tilted phase trellis to always begin and end with the zerostate. Thus, in their solution, the trellis path must return to zerowhen n=N−G. This is accomplished by using l_(t) tail symbols x_(N−G−l)_(t) ₊₁, x_(N−G−l) _(t) ₊₂, . . . , x_(N−G) to flush the state memory ofthe CPE so that it returns the encoder to the zero state at N−G. Thelength l_(t) depends on the tilted phase trellis structure, and is equalto the maximum number of inputs needed to return the path to the zerostate from any other trellis state. Binary response CPM with h=Q/P (Qand P integers) requires the number of tail bits to satisfy theequation: l_(t)≧_(max){L,P−1} M-ary partial-response with h=Q/P requiresthat

$l_{t} \geq {\max {\left\{ {L,\left\lceil \frac{P - 1}{M - 1} \right\rceil} \right\}.}}$

( ┌x┐) is the smallest integer greater than or equal to x).

At the end of the data block, a second length-l_(t) tail sequence isused to ensure that the last state is the zero state. Thus, out of thelength-N symbol sequence, {x_(n)}, there are 2l_(t) tail symbols andN−2l_(t) information symbols. After insertion of the tail bits, thecyclic prefix is pre-pended by copying the last G symbols of {x_(n)} tothe beginning of the block. Thus, the symbol sequence, with guardinterval included is

x _(n) =x _((n)) _(N) , n=−G,−G+1, . . . , −1,0,1, . . . , N−1,   (5)

where (n)_(N) is the residue of n modulo-N and the length-(N+G) sequenceis applied to the CPM modulator that begins in the zero-state. Becauseof the tail symbols, the path through the tilted phase trellis starts atthe zero state when n=−G and returns to the zero state at epochs n=−1,n=N−G, and n=N−1. The trellis path from n=−G to n=−1 is identical tothat from n=N−G to n=N−1.

Although Tan and Stüber do provide one simple example of how to solvefor the tail bits when the transmitter uses GMSK (which is a form ofbinary single-h CPM), they do not discuss a general solution to thisproblem. The problem is that there is no way to formulate a simple,general solution for M-ary multi-h CPM and since the number of tail bitsis data dependent, the number of them will vary from block to block.

The problem with the Stuber and Tan is easily understood by consideringthe following hypothetical scenario (and referring to FIG. 3): Stuberand Tan look at all possible system states and they determine that themaximum number of tail bits required to return the system to the zerostate from any other state is equal to 5. Then, they fix the size of thetwo tail bit sections TB₁, TB₂ (FIG. 3) to be equal to 5. However,suppose that they want to transmit N−10 data bits which only requires 3tail bits in the section labelled TB₁ of FIG. 3 and 2 tail bits in thesection labelled TB₂ of FIG. 3 to return the system to the zero state.If they simply “stuff” the un-needed tail bit slots with “dummy bits”,then they will be generating two entirely new data sequences precedingthe tail sections and they will most likely need a different sequence oftail bits to return the system to the zero state. They may even need adifferent number of tail bits to return the system to the zero state.So, in order to create their cyclic extension, Stuber and Tan will haveto make the tail section variable which results in a more complexreceiver design, which results in the block size being variable, andwhich results in the receiver having to be told the block size beingused (i.e. causing less bandwidth efficiency). Because of this, itappears that their solution cannot be used in a practical system unlessthey change the transmission to be non-Mary (i.e. by including zeros inthe symbol alphabet).

In F. Pancaldi and G. M. Vitetta, “Equalization Algorithms in theFrequency Domain for CPM Signals”, March 2004, pp. 1-26, Pancaldi andVitetta develop FDE algorithms for binary single-h CPM. Their algorithmsrequire a cyclic extension of the transmitted CPM data blocks. Phasecontinuity is preserved by the use of K “channel” bits that are insertedin the data portion of the block. These special bits are computed basedon bits in the previous and current block. Although some of the bits canbe calculated directly, Pancaldi and Vitetti note that there remainK−L+1 bits (where L denotes the memory of the CPM waveform) that must beselected such that their sum (mod 2π) satisfies the following constraint

$\begin{matrix}{{{\pi \; h{\sum\limits_{i = 0}^{K - L}\; a_{N - K + k}^{(l)}}} = \xi_{l}},} & (6)\end{matrix}$

where ζ_(l)=θ_(N) _(T) ^((l−1))−θ_(N−K+(L−1)) ^((l)), θ_(m) ^(k) denotesthe phase state during the m-th symbol interval of the k-th data block,N_(T) denotes the total block length (which includes the cyclic prefixand the data portion of the block), and N denotes the length of thefirst three sub-blocks (which include the cyclic prefix, a data portionand the K “channel” bits) of a block. Pancaldi and Vitetta recommendthat the solution be memorized in a read-only memory for any possiblevalue of ζ₁ at the transmitter.

In general, this may be a complex problem to solve and it is noted thatthe generalization of this result to M-ary multi-h CPM further increasesits complexity.

Need for a Solution

Finally, there is a need for a better approach to solve theaforementioned phase continuity problem for the following reasons: Therehas been a revival of interest in CPM signaling as an alternative toOFDM because of its spectral efficiency and because it's constantenvelope property allows it to be used with less costly non-linearamplifiers without any signal distortion. In addition, future standardsfor networks like that for IEEE 802.16e, CDMA and GSM based networks,may develop special modes that promote the use of CPM waveforms.Moreover, with the rising popularity of DFT-based SC-FDE techniques andthe recent interest in extending these techniques to CPM waveforms, itshould be expected that any future standard that incorporates CPM willconstruct specifications for how the transmitter should incorporate acyclic extension (prefix or postfix) into the CPM waveform. Since thecurrent state of the art discussed above requires the CPM transmitter todo calculations based on past symbols or to do a table-lookup in orderto create a cyclic extension, there is need for a simpler method thatdoes not require any calculations or table look-up and which couldconceivably be adopted as an alternative method by a future standardsbody.

SUMMARY OF THE INVENTION

This invention provides a new and unique method and apparatus to appenda cyclic extension to a continuous phase modulation (CPM) block, whichfeatures transmitting each information symbol and its antipodalcounterpart in any order within a data portion of the continuous phasemodulation block. In operation, the continuous phase modulation blockmay include a sequence of N/2 M-ary information symbols that are spreadover N symbol intervals, the cyclic extension may include the first GM-ary symbols sent in the data portion of the block being appended tothe continuous phase modulation block, and the same modulation index isused for each information symbol and its antipodal counterpart.

The present invention preserves the continuous phase property of a CPMwaveform signal, and provides a solution that is low in complexity,which makes it particularly attractive for use in uplink signallingapplications in broadband multi-user communication networks, WLANs andother suitable communication networks when battery power may be one ofthe most important concerns. Furthermore, according to the presentinvention, there is no need to formally calculate the data-dependentsymbols, either from past information symbols or from a table-lookup.Hence, it represents a lower complexity alternative to the current stateof the art. Finally, the present invention facilitates the use ofDFT-based SC-FDE techniques by the CPM receiver, which leads to a lowercomplexity for channel equalization.

The present invention also introduces redundancy into the transmissionblock which may lead (under certain channel conditions) to improvedreceiver performance vis-à-vis other CPM schemes that do not incorporateany form of redundancy. Thus, implementation of this invention canpotentially achieve similar advantages as those gained by other systemsthat employ spreading techniques at the expense of a lower data rate(such as conjugate-symmetric OFDM).

The present invention provides a low complexity method and apparatus toappend a cyclic extension to a CPM block so that the receiver canequalize the channel using DFT-based linear SC-FDE receiver techniques,by spreading spread an arbitrary sequence of N/2 M-ary informationsymbols—{I₀, I₁, . . . I_(N/2−1)}—over N symbol intervals such that aCPM transmitter can append the cyclic extension without having tocalculate any special “channel” symbols. By doing so, the presentinvention makes the cyclic extension of CPM block transmissions asstraightforward to implement as it is in linearly modulated systems,such as OFDM.

By transmitting each information symbol and its antipodal counterpart(i.e. I_(n) and −I_(n)) in any order within the data portion of theblock, one can force the CPM waveform to return to its initial phasestate (which is observed at the beginning of the data block) after Nsymbols have been transmitted. It follows that once the phase hasreturned to its initial state, that the cyclic postfix can be appendedto the end of the information sequence without disrupting the phasecontinuity of the waveform. Within the scope of the present invention,there are countless ways to transmit the sequence of information symbolsand their antipodal counterparts within the same data block. In onespecial implementation, for example, the N symbols and the correspondingmodulation indices that are used for the CPM block transmission can beconstructed follows:

$\begin{matrix}{{x = \left\{ {\underset{\underset{N\mspace{14mu} {Data}\mspace{14mu} {Symbols}}{}}{I_{0},I_{1},\ldots \mspace{14mu},I_{{N/2} - 1},{- I_{{N/2} - 1}},\ldots \mspace{14mu},{- I_{1}},{- I_{0}}},\underset{\underset{{Length}\text{-}G\mspace{14mu} {Cyclic}\mspace{14mu} {Extension}}{}}{I_{0},I_{1},\ldots \mspace{14mu},I_{G - 1}}} \right\}}{h = \left\{ {\underset{\underset{{Length}\text{-}N\mspace{14mu} {Sequence}}{}}{h_{{(0)}_{J}},h_{{(1)}_{J}},\ldots \mspace{14mu},h_{{({{N/2} - 1})}_{J}},h_{{({{N/2} - 1})}_{J}},\ldots \mspace{14mu},h_{{(1)}_{J}},h_{{(0)}_{J}}},\underset{\underset{{Length}\text{-}G\mspace{14mu} {Cyclic}\mspace{14mu} {Extension}}{}}{h_{{(0)}_{J}},h_{{(1)}_{J}},\ldots \mspace{14mu},h_{{({G - 1})}_{J}}}} \right\}}} & (7)\end{matrix}$

The notation (n)_(J) denotes n mod J. In this special implementation,one may assume that over the first N/2 symbol intervals that themodulation index is allowed to cycle through its J values {h_(J), . . ., h_(J−1)}, or to assume its values over the first N/2 symbol intervalsaccording to rules that are predefined by a system specification. Overthe next N/2 symbol intervals, the modulation indices are reversed. Thiseffectively constrains each symbol and its antipodal counterpart to usethe same modulation index.

In general, as long as the same modulation index is used for I_(n) andfor its antipodal counterpart −I_(n), one can force the phase to returnto its initial state after N symbol intervals.

In effect, the present invention is based of the following observationthat if Φ(t) is a periodic function with period NT, then Φ(t) mod 2π isalso periodic with a period that is an integer multiple of NT. Asdiscussed above, the CPM waveform signal that has a periodic argumentcan be expressed as:

$\begin{matrix}{{{s(t)} = {\exp \left( {{j\Phi}(t)} \right)}}{{\Phi (t)} = {2\pi {\sum\limits_{i = {- \infty}}^{\infty}\; {h_{{(i)}_{J}}I_{{(i)}_{N}}{q\left( {t - {iT}} \right)}}}}}} & (8)\end{matrix}$

However, in order to solve the CPM phase continuity problem, one doesnot require periodicity over all time. Instead, one simply wants toforce the CPM waveform signal to appear to be periodic during the k-thblock (kT, kT+NT+GT), where N denotes the number of M-ary symbols sentin the data portion of the block and G denotes the length of the cyclicextension.

In view of this, the present invention may be implemented by:

1. Fixing J (the number of modulation indices in a multi-h scheme) to bea factor of N. Otherwise, Φ(t) mod 2π will have a period that is >NT.

2. Transmitting N/2 M-ary symbols and their N/2 antipodal counterpartsin any order within the block. This forces the cumulative phase argumentto always sum to zero every N symbols as long as the modulation indexused with an M-ary symbol is also used with its antipodal counterpart.The time-varying part of the phase argument will repeat as well after Nsymbols.

3. Appending the first G M-ary symbols sent in the data portion of theblock as the cyclic extension.

In order to add a cyclic extension (postfix) to the signal withoutdisrupting the continuous phase property of the signal, a length-N datablock is transmitted that contains N/2 M-ary symbols and their antipodalcounterparts in any order. Hence, the block contains:

{I₀, I₁, . . . , I_(N/2−1)}, {−I_(N/2−1), −I_(N/2−2), . . . , −I₀}

The associated modulation indices (which cycle through J differentvalues) are:

{h₍₀₎ _(J) , h₍₁₎ _(J) , . . . , h_((N/2−1)) _(J) }, {h_((N/2−1)) _(J) ,. . . , h₍₁₎ _(J) , h₍₀₎ _(J) }^(→(n)) ^(J) ^(denotes n mod J)

This causes the phase state to always return to its initial value afterN M-ary symbols have been sent, which is the preface required to createa cyclic extension without disrupting the signal's phase.

So after transmitting N M-ary symbols, the first G symbols sent in thedata portion of the block are appended as the cyclic extension. Forexample, the symbols transmitted may be in the following order:

$\left\{ {\underset{\underset{{NM}\text{-}{arySymbols}}{}}{I_{0},I_{1},\ldots \mspace{14mu},I_{{N/2} - 1},{- I_{{N/2} - 1}},{- I_{{N/2} - 2}},\ldots \mspace{14mu},{- I_{0}}},\underset{\underset{\begin{matrix}{{Length}\mspace{14mu} G\mspace{14mu} {Cyclic}} \\{Extension}\end{matrix}}{}}{I_{0},I_{1},\ldots \mspace{14mu},I_{G - 1}}} \right\}$

The present invention is flexible and can be used to construct a cyclicpostfix extension or a cyclic prefix extension.

The present invention also includes a wireless network having a networknode, point or element with a module to append a cyclic extension to acontinuous phase modulation (CPM) block, wherein each information symboland its antipodal counterpart is transmitted in any order within a dataportion of the continuous phase modulation block. The wireless networkmay take the form of a Metropolitan Area Network (MAN) including thatset forth according to the IEEE 802.16e Specification, as well as someother suitable network based on one or more of the 3GPP2, GSM, OFDM orCDMA network configurations.

The present invention also includes a network node, point or element,such as a CPM transmitter or a CPM receiver, having corresponding lowcomplexity cyclic extension modules for respectively transmitting,receiving and/or processing the CPM transmission block according to thepresent invention.

The present invention also includes a computer program product with aprogram code, which program code is stored on a machine readablecarrier, for carrying out the steps of a method comprising one or moresteps for or transmitting each information symbol and its antipodalcounterpart in any order within a data portion of the continuous phasemodulation block, when the computer program is run in a module of eithera network node, point or element in a wireless network.

The present invention also includes implementing the one or more stepsof the method via a computer program running in a processor, controlleror other suitable module in one or more network nodes, points, terminalsor elements in the wireless network.

In summary, the method or apparatus according to the present inventionappends a cyclic extension to a CPM transmission block in a manner thatpreserves the continuous phase property of the signal. In general, ifthe data is sent in any order, then the invention allows one to append acyclic postfix; however, if the data symbols are transmitted in aspecific order, then the invention allows for the construction of acyclic prefix as well. Moreover, the present invention provides asolution that is low in complexity, that is ideal for uplinktransmissions, where battery life is important and that makes the cyclicextension of CPM as simple to implement as it is for OFDM and other,linear single-carrier systems. Moreover, the present invention does notrequire the transmitter to calculate any “channel” symbols. Hence, itrepresents a lower complexity alternative to the current state of theart, is applicable to any form of CPM, whereas the state of the artsolutions have focused on binary single-h CPM, and this invention alsoallows one to use a fixed block size whereas the Stuber/Tan solutiondoes not if they transmit M-ary (no 0's in the alphabet). Moreover, thepresent invention facilitates the use of DFT-based SC-FDE techniques atthe receiver, and could conceivably be a part of future standards for a“low-complexity, low-power” mode.

Furthermore, the present invention advantageously introduces redundancyinto the transmission block which may lead (under certain channelconditions) to improved receiver performance vis-à-vis other CPM schemesthat do not incorporate any form of redundancy. Thus, implementation ofthis invention can potentially achieve similar advantages as thosegained by other systems that employ spreading techniques at the expenseof a lower data rate (such as conjugate-symmetric OFDM). Although thereis a symbol rate reduction of ½, this invention may still offer a higherdata rate and better spectral efficiency than any of the publishedapproaches to the construction of cyclic prefixes for CPM because thosesolutions rely on the use of BINARY single-h CPM. The MBOA's (MultibandOFDM Alliance's) MB-OFDM (Multi-Band OFDM) UWB radio has a specificationwhich is widely accepted by the UWB industry (802.15.3a proposal). Inits 53.3, 55 and 80 Mbps data modes, sends each conjugate-symmetric OFDMsymbol over two consecutive time slots. This represents a spreadingfactor of 4. In addition, for all other data modes below 480 Mbps, theMBOA MB-OFDM UWB radio uses conjugate symmetry. This represents aspreading factor of 2. Thus, this is a good example of the use ofredundancy at the transmitter being acceptable as an industry standard.

BRIEF DESCRIPTION OF THE DRAWING

The drawing includes the following Figures, which are not necessarilydrawn to scale:

FIG. 1 shows an illustration of one block of data, which has beenconstructed to have either a cyclic postfix or prefix, and the windowover which the signal may be processed to obtain an equivalent receiveroutput.

FIG. 2 shows an example of a blind introduction of a cyclic extension,which can destroy the continuous phase property of the CPM waveformsignal.

FIG. 3 shows a diagram of one CPM block (which is an example of theprior art system that has been designed for a binary single-h CPMsystem) having N bits or symbols and a cyclic prefix.

FIG. 4 shows a cyclically extended 4-ary CPM with h=[ 1/16].

FIG. 5 shows a cyclically extended 4-ary CPM with h=¼, N=32 and G=16.

FIG. 6 shows a cyclically extended 4-ary CPM with h=[¼, 1/16], N=32 andG=16.

FIG. 7, including FIGS. 7 a and 7 b, shows an interpretation of thereceived signal as having either a cyclic prefix or postfix when theM-ary symbols are sent in a special order.

FIG. 8 shows a block diagram of an IEEE 802.16e simple campusconfiguration which may be adapted according to the present invention.

FIG. 9, including FIGS. 9 a and 9 b, shows a block diagram of a CPMtransmitter and a CPM receiver according to the present invention.

The description below also includes Figures showing various formats forillustrating the present invention.

BEST MODE OF THE INVENTION

The present invention provides a new and unique method and apparatus toappend a cyclic extension to a continuous phase modulation (CPM) block,featuring transmitting each information symbol and its antipodalcounterpart in any order within a data portion of the continuous phasemodulation block. In operation, the continuous phase modulation blockmay include a sequence of N/2 M-ary information symbols that are spreadover N symbol intervals, the cyclic extension may include the first GM-ary symbols sent in the data portion of the block being appended tothe continuous phase modulation block, and the same modulation index isused for each information symbol and its antipodal counterpart. Thescope of the invention is intended to include embodiments where the samemodulation indices used for the first G-symbols of the data portion ofthe continuous phase modulation block are used for the cyclic extension,as well as where the modulation index of the continuous phase modulationwaveform is determined by the data being sent or other transmissionrule.

The Basic Implementation

In particular, the present invention generates a cyclic extension to aCPM waveform in the guard interval after each block transmission. Hence,it is first important to understand, quite generally, how one can forcea CPM signal to repeat with a certain periodicity.

Forcing the CPM Phase Argument to be Periodic

Let one consider a special CPM waveform, s(t), which has as itsargument, a periodic phase function:

$\begin{matrix}{{{s(t)} = {\exp \left( {{j\Phi}(t)} \right)}}{{\Phi (t)} = {2\pi {\sum\limits_{i = {- \infty}}^{\infty}\; {h_{{(i)}_{J}}I_{{(i)}_{N}}{q\left( {t - {iT}} \right)}}}}}} & (9)\end{matrix}$

where I_((i)) _(N) is an M-ary symbol from the periodic sequence {I₀, .. . , I_(N−1)}, h_((i)) _(N) ∈ {h₀, . . . , h_(J−1)} is a modulationindex from the periodic sequence {h₀, . . . , h_(J−1)}, and the notation(i)_(J) denotes i modulus J. The phase function, q(t) is defined as theintegral of a frequency function, f(t):

$\begin{matrix}{{{q(t)} = {\int_{0}^{t}{{f(\tau)}\ {\tau}}}}{{q(t)} = {{{1/2}\mspace{14mu} {for}\mspace{14mu} t} \geq {{LT}.}}}} & (10)\end{matrix}$

Since {I₀, . . . , I_(N−1)} and {h₀, . . . , h_(J−1)} are periodic,their product sequence h_((i)) _(J) I_((i)) _(N) is also a periodicsequence whose period will be an integer multiple of each of theindividual periods, N and J.

Let one restrict J to be a factor of N. Then, it follows that thefunction Φ(t) is periodic over the interval NT and that the functionΦ(t) mod 2π will also have a period that is an integer multiple of NTbecause the product sequence repeats itself after every N samples. Forexample, if one lets J=2 and N=4, then the product sequence will repeatafter every N=4 samples, as shown below:

$\begin{matrix}{\left\{ {{\ldots \; \underset{\underset{{Fundamental}\mspace{14mu} {Period}}{}}{{h_{0}I_{0}},{h_{1}I_{1}},{h_{0}I_{2}},{h_{1}I_{3}}}},{h_{0}I_{0}},\ldots}\mspace{14mu} \right\}.} & (11)\end{matrix}$

The simplest method of determining the periodicity of Φ(t) mod 2π is tolook at N terms of its argument, for which t-iT≧LT and to compute theirsum mod 2π. This requires us to consider the cumulative phase term atthe n-th and (n+N)-th symbol intervals:

$\begin{matrix}{{\theta_{n - L} = {\left( {\pi {\sum\limits_{i = {- \infty}}^{n - L}\; {h_{{(i)}_{J}}I_{{(i)}_{N}}}}} \right){mod}\; 2\pi}}\begin{matrix}{\theta_{n + N - L} = {\left( {\pi {\sum\limits_{i = {- \infty}}^{n + N - L}\; {h_{{(i)}_{J}}I_{{(i)}_{N}}}}} \right){mod}\; 2\pi}} \\{= {\left( {{\pi {\sum\limits_{i = {- \infty}}^{n - L}\; {h_{{(i)}_{J}}I_{{(i)}_{N}}}}} + {\sum\limits_{i = {- \infty}}^{n + N - L}{h_{{(i)}_{J}}I_{{(i)}_{N}}}}} \right){mod}\; 2\pi}}\end{matrix}} & (12)\end{matrix}$

In the last equation, the latter N-term sum is dependent on the productof two periodic sequences, and is guaranteed to be exactly equal to zerowhenever

$\begin{matrix}{{\sum\limits_{i = {n - L + 1}}^{n + N - L}{h_{{(i)}_{J}}I_{{(i)}_{N}}}} = 0} & (13)\end{matrix}$

When this sum is equal to zero, then the function Φ(t) mod 2π will beperiodic over the interval NT since it will return to the same phasestate after the observation of N symbols. This observation is offundamental importance to the development of the present invention.

Application to Cyclic Extension

The aforementioned description demonstrates that one can force the phaseargument of the CPM waveform mod 2π to have a period of NT. In thediscussion below, it is shown how this observation can be applied to CPMblock transmissions in order to easily construct a cyclic extension.

One assume that the CPM system associates each interval of length (N+G)Twith one block, where N denotes the number of symbols being sent and Gdenotes the number of symbols sent during the cyclic extension.

Forcing the summation in equation (12) to be equal to zero is easilyaccomplished if one takes the N-length transmission block and use it totransmit the following two length N/2 M-ary sequences:

{I₀, . . . , I_(N/2−1)}, {−I₀, . . . , −I_(N/2−1)}.   (14)

There is no constraint on the order in which the elements of these twosets of symbols are to be placed within the data block. The onlyconstraint is that the modulation index associated with I_(n) is alsoused with −I_(n) so that the summation in (12) is equal to zero.

In one implementation, for example, the N symbols transmitted in thedata portion of the block can be expressed as:

y _(n) =I _(n) n=0, . . . , N/2−1

y _(n) =−I _(N−n−1) n=N/2, . . . , N−1   (15)

In order to create the cyclic extension, the transmitter can simplyappend the first G symbols, y₀, . . . , y_(G−1), to the transmissionblock.

Continuing the present example from Eq. (14), the transmitter mightarrange the M-ary symbols (and the modulation indices) within the l-thtransmitted block as follows:

$\begin{matrix}{{x = \left\{ {\underset{\underset{{({1 - 1})}\text{-}{st}\mspace{14mu} {Block}}{}}{\ldots \mspace{20mu} I_{G - 1}^{({l - 1})}},\underset{\underset{{Data}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} 1\text{-}{th}\mspace{14mu} {Block}}{}}{\begin{matrix}{I_{0}^{(l)},I_{1}^{(l)},\ldots \mspace{14mu},I_{{N/2} - 1}^{(l)},} \\{{- I_{{N/2} - 1}^{(l)}},\ldots \mspace{14mu},{- I_{1}^{(l)}},{- I_{0}^{(l)}}}\end{matrix}},\underset{\underset{\begin{matrix}{{Cyclic}\mspace{14mu} {Guard}\mspace{14mu} {Interval}} \\{{for}\mspace{14mu} {the}\mspace{14mu} 1\text{-}{th}\mspace{14mu} {Block}}\end{matrix}}{}}{I_{0}^{(l)},I_{1}^{(l)},\ldots \mspace{14mu},I_{G - 1}^{(l)}},\underset{\underset{\begin{matrix}{{Data}\mspace{14mu} {for}\mspace{14mu} {the}} \\{{({1 + 1})}\text{-}{st}\mspace{14mu} {Block}}\end{matrix}}{}}{I_{0}^{({l + 1})},I_{1}^{({l + 1})},\ldots}} \right\}}{h = {\left\{ {\underset{\underset{{({1 - 1})}\text{-}{st}\mspace{14mu} {Block}}{}}{\ldots \mspace{14mu} h_{{({G - 1})}_{J}}},\underset{\underset{1\text{-}{th}\mspace{14mu} {Block}}{}}{\begin{matrix}{h_{{(0)}_{J}},h_{{(1)}_{J}},\ldots \mspace{14mu},h_{{({{N/2} - 1})}_{J}},} \\{h_{{({{N/2} - 1})}_{J}},\ldots \mspace{14mu},h_{{(1)}_{J}},} \\{h_{{(0)}_{J}},h_{{(0)}_{J}},h_{{(1)}_{J}},\ldots \mspace{14mu},h_{{({G - 1})}_{J}}}\end{matrix}},\underset{\underset{{({1 + 1})}\text{-}{st}\mspace{14mu} {Block}}{}}{h_{{(0)}_{J}},h_{{(1)}_{J}},\ldots}} \right\}.}}} & (16)\end{matrix}$

It is noted that for this special arrangement of symbols within the datablock (shown in Eq. (15)) that one can generate a cyclic prefix orpostfix to the signal, depending on how one wants to process the signal.This property is revealed in the supporting figures discussed below.

EXAMPLES

FIG. 4 shows a cyclically extended 4-ary CPM with h= 1/16. In thisexample, the M-ary symbols and their antipodal counterparts are sent ina random order within each data block, and phase continuity is preservedat the boundary between the data portion of the block and the cyclicextension, as shown.

FIG. 5 shows a cyclically extended 4-ary CPM with h=¼, N=32 and G=16,where N equals the size of the data portion of the block, G equals thesize of the cyclic extension and J equals 1 (the number of modulationindices). FIG. 5 shows the imaginary part of the complex baseband CPMwaveform that has been cyclically extended. The cyclic extensionproperty also exists for the real part of the waveform, which is 4-aryCPM with h=¼, L=3, raised cosine. The CPM waveform signal has acontinuous phase in the transition from the data to the cyclicextension.

FIG. 6 shows a cyclically extended 4-ary CPM with h=[¼, 1/16], N=32 andG=16, where N equals the size of the data portion of the block, G equalsthe size of the cyclic extension, J equals 2 (the number of modulationindices). FIG. 6 shows the real part of the complex baseband CPMwaveform that has been cyclically extended. The cyclic extensionproperty also exists for the imaginary part of the waveform, which is4-ary CPM with h=[¼, 1/16], L=3, raised cosine. The CPM waveform signalhas a continuous phase is the transition from the data to the cyclicextension.

FIG. 7, including FIGS. 7 a and 7 b, shows interpretations of thereceived signal as having either a cyclic prefix or postfix when theM-ary symbols are sent in a special order. When the M-ary symbols aretransmitted in the specific order:

$\left\{ {\underset{\underset{{NM} - {arySymbols}}{}}{I_{0},I_{1},\ldots \mspace{14mu},I_{{N/2} - 1},{- I_{{N/2} - 1}},{- I_{{N/2} - 2}},\ldots \mspace{14mu},{- I_{0}}},\underset{\underset{\begin{matrix}{{Length}\mspace{14mu} G\mspace{14mu} {Cyclic}} \\{Extension}\end{matrix}}{}}{I_{0},I_{1},\ldots \mspace{14mu},I_{G - 1}}} \right\},$

then one can process the same received signal as either having a cyclicpostfix or a cyclic prefix, as shown in FIGS. 7 a and 7 b respectively.

Applications

The present invention may be implemented is a wireless network having anetwork node, point or element with a module to append a cyclicextension to a continuous phase modulation (CPM) block, wherein eachinformation symbol and its antipodal counterpart is transmitted in anyorder within a data portion of the continuous phase modulation block.The wireless network may take the form of a Metropolitan Area Network(MAN) including that set forth according to the IEEE 802.16eSpecification, as well as some other suitable network based on one ormore of the 3GPP2, GSM, OFDM or CDMA network configurations.

For example, FIG. 8 shows an example of one such network configurationin the form of an IEEE 802.16e simple campus configuration taken fromChapter 6 (FIG. 6.9) of C. Smith et al., “3G Wireless and WiMax andWi-Fi 802.16 and 802.11,” The McGraw-Hill Companies, Inc. 2005, whichillustrates a subscriber accessing the 2.5G/3G packet data network viaone or more 802.16e broadband links that may be configured according tothe present invention. In the IEEE 802.16e simple campus configurationin FIG. 8, the smart phone, the BTS(a), BTS(b) and router as shown couldbe implemented with transmitter and receivers according to the presentinvention, consistent with that shown in FIGS. 9 a and 9 b below.

The present invention may also be used as a part of the transmissionspecifications for a future standard (such as future IEEE 802.16e, GSM,OFDM or CDMA) that supports CPM as an alternative uplink modulation. Therecent revival of interest in CPM, coupled with the popularity ofDFT-based linear equalisation schemes, makes the present invention animportant contribution for the design of low complexity CPM cyclicextension schemes.

The present invention may be used as a part of the Wimax project withthe intention of introducing it into future IEEE 802.16e networks. Inaddition, embodiment are envisioned in which the present invention maybe used in 3GPP2, which will soon start to look at their next evolution,and where there may be some potential to introduce CPM into those futurenetworks. Moreover, there is also a strong potential for the presentinvention to have applications in GSM to increase its spectralefficiency, since that system currently uses binary single-h CPM (viaGMSK).

The Transmitter/Receiver Node, Point or Element

FIG. 9 a shows an example of a CPM transmitter generally indicated as100 having a low complexity cyclic extension module 102 according to thepresent invention, as well as other transmitter modules 104. Inoperation, the low complexity cyclic extension module 102 appends acyclic extension to a continuous phase modulation (CPM) block, whereineach information symbol and its antipodal counterpart is transmitted inany order within a data portion of the continuous phase modulationblock, consistent with that shown and described herein.

FIG. 9 b shows an example of a CPM receiver generally indicated as 200having a low complexity cyclic extension module 202 according to thepresent invention, as well as other receiver modules 204. In operation,the low complexity cyclic extension module 202 processes the CPMtransmission block received from the CPM transmitter, consistent withthat shown and described herein.

The Basic Receiver/Transceiver Functionality

The basic functionality of the CPM transmitter 100 and the receiver 200according to the present invention may be implemented as follows:

By way of example, and consistent with that described herein, thefunctionality of the modules 102 and 202 may be implemented usinghardware, software, firmware, or a combination thereof, although thescope of the invention is not intended to be limited to any particularembodiment thereof. In a typical software implementation, the module 102and 202 would be one or more microprocessor-based architectures having amicroprocessor, a random access memory (RAM), a read only memory (ROM),input/output devices and control, data and address buses connecting thesame. A person skilled in the art would be able to program such amicroprocessor-based implementation to perform the functionalitydescribed herein without undue experimentation. The scope of theinvention is not intended to be limited to any particular implementationusing technology now known or later developed in the future. Moreover,the scope of the invention is intended to include the modules 102 and202 being used as stand alone modules, as shown, or in the combinationwith other circuitry for implementing another module.

The other modules 104 and 204 and the functionality thereof are known inthe art, do not form part of the underlying invention per se, and arenot described in detail herein.

Advantages/Disadvantages

Advantages of the present invention include the following:

1. The present invention circumvents the need for the transmitter tocalculate tail or channel bits based on the past symbols, which impliesthat the complexity level is much lower than the state of the art.

2. Because the data block contains two copies of each symbol, thepresent invention may be used to improve receiver performance byexploiting the diversity of the received signal.

3. The new method and apparatus to cyclically extend CPM according tothe present invention enables the use of low complexity SC-FDEtechniques at the receiver.

4. The low complexity of the method and apparatus according to thepresent invention helps to remove some of the possible reservationsagainst the use of CPM.

5. The present invention maintains the same level of transmittercomplexity for all CPM variants (i.e. single-h, multi-h, binary, M-ary,etc.), while the state of the art solution increases incomplexity/required memory allocation as the CPM waveform itselfincreases in complexity.

6. With the rising popularity of DFT-based SC-FDE techniques and therecent interest in extending these techniques to CPM waveforms, itshould be expected that any future standard that incorporates CPM willconstruct specifications for how the transmitter should incorporate acyclic extension into the CPM waveform. The present invention addressesthat concern and could be easily used in a low-complexity, low-powermode for CPM data transmission.

One shortcoming of the present invention is that transmitting N/2instead of N data symbols in each data block reduces the throughput by afactor of two. However, there may be situations in which the redundancyof the data actually improves the receiver performance, such as when thelength of the channel exceeds the length of the cyclic extension. Inaddition, there are many well-known systems that use time domainspreading and/or frequency domain spreading (via conjugate symmetry) intheir implementations. One example is the MBOA's (Multiband OFDMAlliance's) MB-OFDM (Multi-Band OFDM) UWB radio, which, in its 53.3, 55and 80 Mbps data modes, sends each conjugate-symmetric OFDM symbol overtwo consecutive time slots.

This represents a spreading factor of 4. In addition, for all other datamodes below 480 Mbps, the MBOA MB-OFDM UWB radio uses conjugatesymmetry. This represents a spreading factor of 2. Hence, the loss indata rate should not be a deterrent to recognising the usefulness ofthis invention.

List of Abbreviations

CPM: Continuous Phase Modulation

ISI: Inter-symbol interference

MBOA: MultiBand OFDM Alliance

MB-OFDM: Multiband OFDM

SC-FDE: Single Carrier Frequency Domain Equalisation

UWB: Ultrawideband

Scope of the Invention

Accordingly, the invention comprises the features of construction,combination of elements, and arrangement of parts which will beexemplified in the construction hereinafter set forth.

It will thus be seen that the objects set forth above, and those madeapparent from the preceding description, are efficiently attained and,since certain changes may be made in the above construction withoutdeparting from the scope of the invention, it is intended that allmatter contained in the above description or shown in the accompanyingdrawing shall be interpreted as illustrative and not in a limitingsense.

1. A method comprising: appending a cyclic extension to a continuous phase modulation block; and transmitting each information symbol and its antipodal counterpart in any order within a data portion of the continuous phase modulation block.
 2. A method according to claim 1, wherein the continuous phase modulation block includes a sequence of N/2 M-ary information symbols that are spread over N symbol intervals.
 3. A method according to claim 1, wherein the cyclic extension includes the first G M-ary symbols that are sent in the data portion of the block being appended to the continuous phase modulation block.
 4. A method according to claim 1, wherein the cyclic extension is appended as a postfix at the end of the information sequence without disrupting the phase continuity of the waveform of the continuous phase modulation block.
 5. A method according to claim 2, wherein the sequence includes over the first N/2 symbol intervals allowing the modulation index to cycle through its J values or to assume its values over the first N/2 symbol intervals according to rules that are predefined by a system specification, and over the next N/2 symbol intervals reversing the modulation indices.
 6. A method according to claim 1, wherein the same modulation index is used for each information symbol and its antipodal counterpart.
 7. A method according to claim 1, wherein the continuous phase modulation waveform has a phase argument that is constructed from the following symbols, their anti-podal counterparts, and the set of modulation indices: {I₀, . . . , I_(N/2−1)}, {−I₀, . . . , −I_(N/2−1)} {h₍₀₎ _(J) , . . . , h_((N/2−1)) _(J) }, {h₍₀₎ _(J) , . . . , h_((N/2−1)) _(J) } where I_(i) is an M-ary symbol from the sequence {I₀, . . . , I_(N/2−1)}, h_((i)) _(N) ∈ {h₀, . . . , h_(J−1)} is a modulation index from the periodic sequence {h₀, . . . , h_(J−1)}, and the notation (i)_(J) denotes i modulus J.
 8. (canceled)
 9. A method according to claim 1, wherein the phase state returns to its initial value after N M-ary symbols have been sent.
 10. A method according to claim 1, wherein the method is used in uplink signalling applications when battery power is an important concern.
 11. A method according to claim 1, wherein the order is random.
 12. (canceled)
 13. (canceled)
 14. (canceled)
 15. (canceled)
 16. (canceled)
 17. (canceled)
 18. (canceled)
 19. (canceled)
 20. (canceled)
 21. (canceled)
 22. (canceled)
 23. A network node, point or element comprising: a module configured to append a cyclic extension to a continuous phase modulation block in a wireless network, each information symbol and its antipodal counterpart being transmitted in any order within a data portion of the continuous phase modulation block.
 24. A network node, point or element according to claim 23, wherein the continuous phase modulation block includes a sequence of N/2 M-ary information symbols that are spread over N symbol intervals.
 25. A network node, point or element according to claim 23, wherein the cyclic extension includes the first G M-ary symbols that are sent in the data portion of the block being appended to the continuous phase modulation block.
 26. A network node, point or element according to claim 23, wherein the cyclic extension is appended as a postfix at the end of the information sequence without disrupting the phase continuity of the waveform of the continuous phase modulation block.
 27. A network node, point or element according to claim 24, wherein the sequence includes over the first N/2 symbol intervals allowing the modulation index to cycle through its J values or to assume its values over the first N/2 symbol intervals according to rules that are predefined by a system specification, and over the next N/2 symbol intervals reversing the modulation indices.
 28. A network node, point or element according to claim 23, wherein the same modulation index is used for each information symbol and its antipodal counterpart.
 29. A network node, point or element according to claim 23, wherein the continuous phase modulation waveform has a phase argument that is constructed from the following symbols, their anti-podal counterparts, and the set of modulation indices: {I₀, . . . , I_(N/2−1)}, {−I₀, . . . , −I_(N/2−1)} {h₍₀₎ _(J) , . . . , h_((N/2−1)) _(J) }, {h₍₀₎ _(J) , . . . , h_((N/2−1)) _(J) } where I_(i) is an M-ary symbol from the sequence {I₀, . . . , I_(N/2−1)}, h_((i)) _(N) ∈ {h₀, . . . , h_(J−1)} is a modulation index from the periodic sequence {h₀, . . . , h_(J−1)}, and the notation (i)_(J) denotes i modulus J.
 30. (canceled)
 31. A network node, point or element according to claim 23, wherein the phase state returns to its initial value after N M-ary symbols have been sent.
 32. A network node, point or element according to claim 23, wherein the continuous phase modulation block is used in uplink signalling applications when battery power is an important concern.
 33. A network node, point or element according to claim 23, wherein the order is random.
 34. A network node, point or element according to claim 23, wherein the network node, point or element is a continuous phase modulation transmitting device for transmitting the continuous phase modulation block.
 35. A network node, point or element according to claim 23, wherein the network node, point or element is a continuous phase modulation receiving device for receiving the continuous phase modulation block.
 36. A network node, point or element according to claim 23, wherein the network node, point or element forms part of a Metropolitan Area Network, or some other suitable network based on a Global System for Mobile communications, othogonal frequency division multiplexing or code division multiple access network configuration.
 37. A computer-readable storage medium having computer-executable components for carrying out a method comprising appending a cyclic extension to a continuous phase modulation block; and transmitting each information symbol and its antipodal counterpart in any order within a data portion of the continuous phase modulation block.
 38. A method according to claim 1, wherein the method further comprises implementing the method via a computer program running in a processor, controller or other suitable module in one or more network nodes, points, terminals or elements in the wireless network.
 39. A wireless network according to claim 12, wherein the wireless network is a Metropolitan Area Network, as well as some other suitable network based on one or more of the Third Generation Partnership Project 2, Global System for Mobile communications, othoqonal frequency division multiplexing or code division multiple access network configurations.
 40. A method according to claim 1, wherein the same modulation indices used for the first G-symbols of the data portion of the continuous phase modulation block are used for the cyclic extension.
 41. A method according to claim 1, wherein the modulation index of the continuous phase modulation waveform is determined by the data being sent or other transmission rule.
 42. A wireless network according to claim 12, wherein the same modulation indices used for the first G-symbols of the data portion of the continuous phase modulation block are used for the cyclic extension.
 43. A wireless network according to claim 12, wherein the modulation index of the continuous phase modulation waveform is determined by the data being sent or other transmission rule.
 44. A wireless node, point or element according to claim 23, wherein the same modulation indices used for the first G-symbols of the data portion of the continuous phase modulation block are used for the cyclic extension.
 45. A wireless node, point or element according to claim 23, wherein the modulation index of the continuous phase modulation waveform is determined by the data being sent or other transmission rule.
 46. Apparatus comprising: means for appending a cyclic extension to a continuous phase modulation block; and means for transmitting each information symbol and its antipodal counterpart in any order within a data portion of the continuous phase modulation block.
 47. A module comprising: one or more elements configured for appending a cyclic extension to a continuous phase modulation block and for transmitting each information symbol and its antipodal counterpart in any order within a data portion of the continuous phase modulation block.
 48. A module according to claim 47, wherein the module forms part of a continuous phase modulation transmitter. 